3,776 research outputs found
On the existence of a solution to a spectral estimation problem \emph{\`a la} Byrnes-Georgiou-Lindquist
A parametric spectral estimation problem in the style of Byrnes, Georgiou,
and Lindquist was posed in \cite{FPZ-10}, but the existence of a solution was
only proved in a special case. Based on their results, we show that a solution
indeed exists given an arbitrary matrix-valued prior density. The main tool in
our proof is the topological degree theory.Comment: 6 pages of two-column draft, accepted for publication in IEEE-TA
Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation
We use elliptic Taylor series expansions and interpolation to deduce a number
of summations for elliptic hypergeometric series. We extend to the well-poised
elliptic case results that in the -case have previously been obtained by
Cooper and by Ismail and Stanton. We also provide identities involving S.
Bhargava's cubic theta functions
Recursive bayesian identification of nonlinear autonomous systems
This paper concerns the recursive identification of nonlinear discrete-time systems for which the original equations of motion are not known. Since the true model structure is not available, we replace it with a generic nonlinear model. This generic model discretizes the state space into a finite grid and associates a set of velocity vectors to the nodes of the grid. The velocity vectors are then interpolated to define a vector field on the complete state space. The proposed method follows a Bayesian framework where the identified velocity vectors are selected by the maximum a posteriori (MAP) criterion. The resulting algorithms allow a recursive update of the velocity vectors as new data is obtained. Simulation examples using the recursive algorithm are presented
Non-linear minimum variance estimation for discrete-time multi-channel systems
A nonlinear operator approach to estimation in discrete-time systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model may also include a communications channel involving either static or dynamic nonlinearities. The signal channel is represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement
- …